Abstract : The symmetric wave theory is applied to a twoisentropic-layer model of the atmosphere. The non-rotating two-layer model is used to examine the justification for the quasi-solenoidal approximation and the vertical quasi-symmetry approximation which is introduced in the subsequent theory. The non-geostrophic theory is discussed for symmetric waves in an atmosphere with constant rotation (zero planetary vorticity gradient). The physical interpretation of the behavior of the waves is emphasized. (Author)